Redknapp hopes the prospect of playing alongside Rio Ferdinand, who signed from Manchester United on Thursday, will entice Caulker to join the west London club, who have replaced relegated Cardiff in the Premier League.
"He's got a couple of other clubs interested in him but I think he feels if he was playing with Rio, it could help him get back into the England team," said Redknapp, who worked with Caulker when they were at Tottenham Hotspur together.
The 22-year-old has made one appearance for England, scoring against Sweden in 2012.
Redknapp added that Ryan Giggs, who was caretaker manager at Manchester United towards the end of last season, told him that Ferdinand would have been his number one central defender if he had been given the job on a full-time basis.
Reports in Italy claim that QPR are hoping to sign the 24-year-old with Redknapp having been impressed with Bonaventura's performances last season.
The Italy international scored five times and set up four others in 31 league appearances to help Atalanta finish 11th in Serie A.
"I have read of a possible interest from Queens Park Rangers on Bonaventura," Bonaventura's agent Giocondo Martorelli was quoted as saying by www.tuttomercatoweb.com. "However, I have spoken to (Atalanta general manager Pierpaolo) Marino and he has not mentioned to me this option."
Bonaventura, a product of Atalanta's youth system, has been linked with a move away from Bergamo this summer with Fiorentina also among the clubs reportedly keen to acquire his services.
He is under contract with the Bergamaschi until June 2017.
- Sports & Recreation
- Rio Ferdinand
- Manchester United
- Giacomo Bonaventura
- Queens Park Rangers
- Tottenham Hotspur